Key research themes
1. How can robust and reduced-order fractional infinite impulse response filters be designed for complex dynamical systems with memory effects and uncertainties?
This research area focuses on designing fractional-order infinite impulse response (IIR) filters that accommodate the memory and hereditary properties intrinsic to fractional dynamical systems. These filters aim to achieve reduced order, improved stability, and robustness against time delays, impulses, and uncertainties commonly present in singular fractional-order systems and neural networks. The theme addresses theoretical conditions for admissibility, H∞ filtering performance, and stability, employing methods such as linear matrix inequalities (LMIs), Caputo fractional derivatives, and impulsive differential equations. This is crucial for practical control and signal processing applications where fractional dynamics better represent physical realities compared to integer-order models.
2. What are computational strategies to accurately design and analyze infinite impulse response filters under finite precision constraints and fractional order dynamics?
This theme explores advanced computational methods for designing and assessing IIR filters, especially under the challenges of finite-precision arithmetic, coefficient quantization, and fractional-order dynamics. It investigates interval arithmetic approaches to quantify the effects of quantization on filter frequency responses, as well as approximation and implementation methods for fractional filters of arbitrary order to enable fully controllable frequency responses. Addressing these computational and approximation challenges is essential to ensure practical realizations of fractional IIR filters meet stringent performance specifications across hardware platforms.
3. How does fractional calculus and fractional-order system theory influence the dynamic modeling and stability analysis of complex biological and neural networks with impulsive and delayed effects?
This research direction investigates the application of fractional calculus in modeling the dynamics of biological systems, gene regulatory networks, and neural networks that exhibit memory effects, delays, and impulsive perturbations. By employing Caputo fractional derivatives and incorporating reaction-diffusion and impulsive dynamics, these studies provide existence, uniqueness, and stability criteria for complex networks with fractional order dynamics. Such models significantly broaden the understanding of fractional behavior in living systems and guide the stability considerations crucial for implementing fractional-order signal processing too.